Here, we present the calculations for the initial design of the DEFUSE3 trial based on [@Lai2014191] and [@Lai201593]. The trial parameters are fixed as follows.
library(ASSISTant)
##Fix randomization vector N, errors, eps
trialParameters <- list(N = c(200, 340, 476), type1Error = 0.025,
eps = 1/2, type2Error = 0.1)The design parameters are the following for various scenarios.
designParameters <- list(
nul0 = list(prevalence = rep(1/6, 6), mean = matrix(0, 2, 6),
sd = matrix(1, 2, 6)),
alt1 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.5, 0.4, 0.3, 0, 0, 0)),
sd = matrix(1, 2, 6)),
alt2 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.5, 0.5, 0, 0, 0, 0)),
sd = matrix(1,2, 6)),
alt3 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6), rep(0.36, 6)),
sd = matrix(1,2, 6)),
alt4 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6), rep(0.30, 6)),
sd = matrix(1,2, 6)),
alt5 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.4, 0.3, 0.2, 0, 0, 0)),
sd = matrix(1,2, 6)),
alt6 = list(prevalence = rep(1/6, 6), mean = rbind(rep(0, 6),
c(0.5, 0.5, 0.3, 0.3, 0.1, 0.1)),
sd = matrix(1,2, 6))
)defuse3 <- DEFUSE3Design$new(trialParameters = trialParameters,
designParameters = designParameters$nul0, showProgress = FALSE)
print(defuse3)## Design Parameters:
## List of 4
## $ prevalence: num [1:6] 0.167 0.167 0.167 0.167 0.167 ...
## $ mean : num [1:2, 1:6] 0 0 0 0 0 0 0 0 0 0 ...
## $ sd : num [1:2, 1:6] 1 1 1 1 1 1 1 1 1 1 ...
## $ J : int 6
## Trial Parameters:
## List of 5
## $ N : num [1:3] 200 340 476
## $ type1Error: num 0.025
## $ eps : num 0.5
## $ type2Error: num 0.1
## $ effectSize: num 0.105
## Boundaries:
## Named num [1:3] -1.88 2.63 2.61
## - attr(*, "names")= chr [1:3] "btilde" "b" "c"
## Data Generating function:
## function (prevalence = rep(1/6, 6), N, mean = matrix(0, 2, 6),
## sd = matrix(1, 2, 6))
## {
## if (N == 0) {
## data.frame(subGroup = integer(0), trt = integer(0), score = numeric(0))
## }
## else {
## subGroup <- sample(seq_along(prevalence), N, replace = TRUE,
## prob = prevalence)
## trt <- sample(c(0L, 1L), N, replace = TRUE)
## rankin <- unlist(Map(function(i, j) rnorm(n = 1, mean = mean[i,
## j], sd = sd[i, j]), trt + 1, subGroup))
## data.frame(subGroup = subGroup, trt = trt, score = rankin)
## }
## }
## <environment: 0x7fb112f7bad8>result <- defuse3$explore(numberOfSimulations = 5000, showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.011200; P(Reject H0_subgp) = 0.016800; P(Reject H0) = 0.028000
## P(Early stop for efficacy [futility]) = 0.016000 [0.744400]
## Mean [SD] Randomized N = 344.081600 [91.690913]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.2036 0.5568 0.2396
##
## Mean [SD] Lost N = 125.678400 [66.904172]
## Mean [SD] Analyzed N = 218.403200 [82.417665]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.0060 0.0058 0.0026 0.0008 0.0016 0.0112
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 56 0 0 0 0 0
## 1 0 1322 741 576 506 588
## 2 0 179 158 156 141 268
## 3 0 30 27 52 64 136
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 166.7617 133.4251 100.3038 66.75889 33.09354
## 2 NA 283.1508 226.9810 169.9551 113.48936 56.94776
## 3 NA 398.0000 312.8889 236.4231 159.90625 79.49265
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.262090 6.976901 7.049370 6.896201 5.289869
## 2 NA 6.810817 8.431418 8.729884 7.711417 7.435432
## 3 NA 6.721043 12.564704 9.933793 10.431513 7.785072
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.262090 6.976901 7.049370 6.896201 5.289869
## 2 NA 6.810817 8.431418 8.729884 7.711417 7.435432
## 3 NA 6.721043 12.564704 9.933793 10.431513 7.785072result <- defuse3$explore(numberOfSimulations = 5000, trueParameters = designParameters$alt1,
showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.326800; P(Reject H0_subgp) = 0.571200; P(Reject H0) = 0.898000
## P(Early stop for efficacy [futility]) = 0.462200 [0.014400]
## Mean [SD] Randomized N = 394.578400 [95.017737]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.1186 0.3580 0.5234
##
## Mean [SD] Lost N = 126.942200 [111.547085]
## Mean [SD] Analyzed N = 267.636200 [107.679367]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.1114 0.1684 0.2312 0.0466 0.0136 0.3268
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 1634 0 0 0 0 0
## 1 0 327 378 383 100 52
## 2 0 138 226 332 86 37
## 3 0 125 299 603 176 104
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 166.9174 134.0952 100.5770 66.6400 32.88462
## 2 NA 282.4855 225.8761 171.1265 113.3140 56.29730
## 3 NA 395.2000 316.3010 238.2803 158.3523 80.25000
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.202869 6.307036 6.819566 6.456568 4.730601
## 2 NA 8.103559 8.040047 9.374821 7.933935 6.054681
## 3 NA 8.918990 10.318568 11.053903 10.395097 8.365150
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.202869 6.307036 6.819566 6.456568 4.730601
## 2 NA 8.103559 8.040047 9.374821 7.933935 6.054681
## 3 NA 8.918990 10.318568 11.053903 10.395097 8.365150result <- defuse3$explore(numberOfSimulations = 5000, trueParameters = designParameters$alt2,
showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.218800; P(Reject H0_subgp) = 0.684000; P(Reject H0) = 0.902800
## P(Early stop for efficacy [futility]) = 0.496600 [0.018200]
## Mean [SD] Randomized N = 392.323200 [90.283621]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.0976 0.4172 0.4852
##
## Mean [SD] Lost N = 161.566800 [113.976931]
## Mean [SD] Analyzed N = 230.756400 [103.036576]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.1166 0.4622 0.0776 0.0208 0.0068 0.2188
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 1094 0 0 0 0 0
## 1 0 362 895 192 81 41
## 2 0 151 687 135 64 40
## 3 0 97 872 163 73 53
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 167.3978 134.1352 101.1562 68.95062 33.7561
## 2 NA 283.9603 227.0247 170.7111 115.95312 57.3750
## 3 NA 394.6907 316.6594 238.8589 159.65753 79.0000
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.551751 6.827914 6.696609 6.268774 5.651462
## 2 NA 6.937705 8.463830 8.232504 8.169688 7.827262
## 3 NA 7.620369 10.098018 11.201784 11.476085 8.678000
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.551751 6.827914 6.696609 6.268774 5.651462
## 2 NA 6.937705 8.463830 8.232504 8.169688 7.827262
## 3 NA 7.620369 10.098018 11.201784 11.476085 8.678000result <- defuse3$explore(numberOfSimulations = 5000, trueParameters = designParameters$alt3,
showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.873600; P(Reject H0_subgp) = 0.055600; P(Reject H0) = 0.929200
## P(Early stop for efficacy [futility]) = 0.751400 [0.015200]
## Mean [SD] Randomized N = 310.758400 [109.553894]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.4356 0.3310 0.2334
##
## Mean [SD] Lost N = 16.931800 [53.698993]
## Mean [SD] Analyzed N = 293.826600 [101.694573]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.0142 0.0108 0.0098 0.0102 0.0106 0.8736
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 4368 0 0 0 0 0
## 1 0 54 41 24 27 55
## 2 0 14 16 17 23 39
## 3 0 18 23 39 76 166
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 166.8889 131.5610 101.2500 65.48148 33.94545
## 2 NA 284.5714 228.5625 166.5294 114.08696 57.84615
## 3 NA 398.2222 319.0435 238.2051 155.55263 79.62651
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.903842 5.835447 6.144987 6.874537 5.085995
## 2 NA 7.397653 7.991402 9.868622 10.334906 7.364704
## 3 NA 7.108864 10.407507 9.509495 9.082430 8.368354
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.903842 5.835447 6.144987 6.874537 5.085995
## 2 NA 7.397653 7.991402 9.868622 10.334906 7.364704
## 3 NA 7.108864 10.407507 9.509495 9.082430 8.368354result <- defuse3$explore(numberOfSimulations = 5000, trueParameters = designParameters$alt4,
showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.726600; P(Reject H0_subgp) = 0.099600; P(Reject H0) = 0.826200
## P(Early stop for efficacy [futility]) = 0.579000 [0.037400]
## Mean [SD] Randomized N = 350.981600 [112.886397]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.2942 0.3222 0.3836
##
## Mean [SD] Lost N = 37.431800 [75.444388]
## Mean [SD] Analyzed N = 313.549800 [105.160805]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.0266 0.0208 0.0166 0.0192 0.0164 0.7266
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 3633 0 0 0 0 0
## 1 0 123 83 64 55 93
## 2 0 46 35 37 66 103
## 3 0 37 55 90 135 345
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 166.0325 132.9880 100.8281 68.07273 34.13978
## 2 NA 282.5000 222.9429 169.7568 114.21212 55.74757
## 3 NA 394.0811 314.9818 237.9889 158.33333 79.04058
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.636437 6.511704 7.358301 6.491746 5.418550
## 2 NA 7.070282 9.486656 8.118584 8.681572 6.609142
## 3 NA 9.373065 10.012013 11.970464 10.154772 7.771712
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.636437 6.511704 7.358301 6.491746 5.418550
## 2 NA 7.070282 9.486656 8.118584 8.681572 6.609142
## 3 NA 9.373065 10.012013 11.970464 10.154772 7.771712result <- defuse3$explore(numberOfSimulations = 5000, trueParameters = designParameters$alt5,
showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.173000; P(Reject H0_subgp) = 0.590600; P(Reject H0) = 0.763600
## P(Early stop for efficacy [futility]) = 0.361000 [0.053400]
## Mean [SD] Randomized N = 408.693600 [87.445390]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.0782 0.3362 0.5856
##
## Mean [SD] Lost N = 149.156000 [102.877708]
## Mean [SD] Analyzed N = 259.537600 [101.979950]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.1742 0.1888 0.1782 0.0388 0.0106 0.1730
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 865 0 0 0 0 0
## 1 0 569 523 440 156 99
## 2 0 242 299 379 131 89
## 3 0 157 319 424 173 135
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 167.4130 133.5143 99.96591 68.40385 33.35354
## 2 NA 282.8926 226.3411 169.71504 114.23664 57.83146
## 3 NA 395.5478 317.6238 236.84670 158.54335 80.68148
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.254767 6.505913 6.953226 6.657306 5.198730
## 2 NA 6.969765 8.627100 8.957753 9.170045 6.465355
## 3 NA 7.965829 10.427778 11.075396 10.630946 8.073036
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.254767 6.505913 6.953226 6.657306 5.198730
## 2 NA 6.969765 8.627100 8.957753 9.170045 6.465355
## 3 NA 7.965829 10.427778 11.075396 10.630946 8.073036result <- defuse3$explore(numberOfSimulations = 5000, trueParameters = designParameters$alt6,
showProgress = FALSE)
analysis <- defuse3$analyze(result)
print(defuse3$summary(analysis))## P(Reject H0_ITT) = 0.702400; P(Reject H0_subgp) = 0.239600; P(Reject H0) = 0.942000
## P(Early stop for efficacy [futility]) = 0.601800 [0.007800]
## Mean [SD] Randomized N = 354.594400 [111.356733]
##
## Stage at exit (proportion)
##
## 1 2 3
## 0.2750 0.3346 0.3904
##
## Mean [SD] Lost N = 53.768600 [95.862006]
## Mean [SD] Analyzed N = 300.825800 [108.616694]
##
## Chance of each subpopulation rejected
##
## 1 2 3 4 5 6
## 0.0352 0.0804 0.0486 0.0600 0.0154 0.7024
##
## Counts by futility stage and subgroup choice
##
## 0 1 2 3 4 5
## 0 3512 0 0 0 0 0
## 1 0 95 142 82 83 48
## 2 0 50 112 56 79 24
## 3 0 41 196 150 226 104
##
## Mean loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 166.4947 133.1127 100.7195 68.25301 34.02083
## 2 NA 282.6400 227.0893 172.1964 115.29114 56.91667
## 3 NA 397.2195 318.2449 238.7333 159.87168 79.62500
##
## SD loss by futility stage and subgroup
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.779409 5.815239 6.896545 7.701510 4.896762
## 2 NA 6.799640 7.902051 9.891079 7.644592 6.198995
## 3 NA 10.150153 10.694414 10.252953 9.637261 7.837163
## 0 1 2 3 4 5
## 0 0 NA NA NA NA NA
## 1 NA 5.779409 5.815239 6.896545 7.701510 4.896762
## 2 NA 6.799640 7.902051 9.891079 7.644592 6.198995
## 3 NA 10.150153 10.694414 10.252953 9.637261 7.837163